How many dimensions do linear equations on the x-y plane have?
Linear equations on the x-y plane have two dimensions.
To understand why, let's break it down step by step:
1. The x-y plane is a two-dimensional plane. It is like a piece of paper with an x-axis (horizontal) and a y-axis (vertical), crossing each other at the origin (0,0).
2. A linear equation on the x-y plane represents a straight line. It is written in the form y = mx + b, where m represents the slope of the line, and b represents the y-intercept (the point where the line intersects the y-axis).
3. In a linear equation, there are two variables, x and y. Each value of x corresponds to a specific value of y that satisfies the equation. So, for every x-coordinate, there is one and only one corresponding y-coordinate on the line.
4. Therefore, linear equations on the x-y plane describe a relationship between two variables within a two-dimensional space.
In summary, linear equations on the x-y plane have two dimensions because they represent the relationship between two variables (x and y) embedded in the two-dimensional x-y coordinate system.